Polynomial Interpolation Problem for Skew Polynomials
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
Let R = K[x;δ] be a skew polynomial ring over a division ring K. We introduce the notion of derivatives of skew polynomial at scalars. An analogous definition of derivatives of commutative polynomials from K[x] as a function of K[x] → K[x] is not possible in a non-commutative case. This is the reason why we have to define the derivative of a skew polynomial at a scalar. Our definition is based on properties of skew polynomial rings, and it makes possible some useful theorems about them. The main result of this paper is a generalization of polynomial interpolation problem for skew polynomials. We present conditions under which there exists a unique polynomial of a degree less then n which takes prescribed values at given points xi Є K (1 ≤ n). We also discuss some kind of Silvester-Lagrange skew polynomia
Кључне речи:
interpolation / skew polynomialsИзвор:
Applicable Analysis and Discrete Mathematics, 2007, 1(2),403-414Колекције
Институција/група
GraFarTY - JOUR AU - Erić, Aleksandra Lj. PY - 2007 UR - https://grafar.grf.bg.ac.rs/handle/123456789/3178 AB - Let R = K[x;δ] be a skew polynomial ring over a division ring K. We introduce the notion of derivatives of skew polynomial at scalars. An analogous definition of derivatives of commutative polynomials from K[x] as a function of K[x] → K[x] is not possible in a non-commutative case. This is the reason why we have to define the derivative of a skew polynomial at a scalar. Our definition is based on properties of skew polynomial rings, and it makes possible some useful theorems about them. The main result of this paper is a generalization of polynomial interpolation problem for skew polynomials. We present conditions under which there exists a unique polynomial of a degree less then n which takes prescribed values at given points xi Є K (1 ≤ n). We also discuss some kind of Silvester-Lagrange skew polynomia T2 - Applicable Analysis and Discrete Mathematics T1 - Polynomial Interpolation Problem for Skew Polynomials VL - 1(2),403-414 DO - 10.2298/AADM0702403E ER -
@article{ author = "Erić, Aleksandra Lj.", year = "2007", abstract = "Let R = K[x;δ] be a skew polynomial ring over a division ring K. We introduce the notion of derivatives of skew polynomial at scalars. An analogous definition of derivatives of commutative polynomials from K[x] as a function of K[x] → K[x] is not possible in a non-commutative case. This is the reason why we have to define the derivative of a skew polynomial at a scalar. Our definition is based on properties of skew polynomial rings, and it makes possible some useful theorems about them. The main result of this paper is a generalization of polynomial interpolation problem for skew polynomials. We present conditions under which there exists a unique polynomial of a degree less then n which takes prescribed values at given points xi Є K (1 ≤ n). We also discuss some kind of Silvester-Lagrange skew polynomia", journal = "Applicable Analysis and Discrete Mathematics", title = "Polynomial Interpolation Problem for Skew Polynomials", volume = "1(2),403-414", doi = "10.2298/AADM0702403E" }
Erić, A. Lj.. (2007). Polynomial Interpolation Problem for Skew Polynomials. in Applicable Analysis and Discrete Mathematics, 1(2),403-414. https://doi.org/10.2298/AADM0702403E
Erić AL. Polynomial Interpolation Problem for Skew Polynomials. in Applicable Analysis and Discrete Mathematics. 2007;1(2),403-414. doi:10.2298/AADM0702403E .
Erić, Aleksandra Lj., "Polynomial Interpolation Problem for Skew Polynomials" in Applicable Analysis and Discrete Mathematics, 1(2),403-414 (2007), https://doi.org/10.2298/AADM0702403E . .